# Write a system of equations to model each situation in life NEXT To describe a word problem using a system of equations, we need to figure out what the two unknown quantities are and give them names, usually x and y. Sample Problem Set up a system of equations describing the following problem: A woman owns 21 pets. Each of her pets is either a cat or a bird.

There are two unknown quantities here: The problem has given us two pieces of information: Let x be the number of cats the lady owns, and y be the number of birds the lady owns. Now we can replace the pieces of information with equations. Instead of saying "if we add the number of cats the lady owns and the number of birds the lady owns, we get 21, " we can say: Since a cat has 4 legs, if the lady owns x cats there are 4x cat legs.

Since a bird has 2 legs, if the lady owns y cats there are 2y bird legs.

## Writing a System of Equations

This means we can replace this second piece of information with an equation: In this problem, x meant the number of cats and y meant the number of birds.

In order to have a meaningful system of equations, we need to know what each variable represents. Well, that or spending a semester studying abroad in Mathrovia.

Sample Problem Write a system of equations describing the following word problem: The Lopez family had a rectangular garden with a 20 foot perimeter. They enlarged their garden to be twice as long and three feet wider than it was originally.

They had to, since their cherry tomato plants were getting out of control. The enlarged garden has a 40 foot perimeter. What were the dimensions of the original garden? The problem asks "What were the dimensions of the original garden?

Our first piece of information is that the original garden had a 20 foot perimeter.Write a system of equations to represent the situation and solve. Define your variables. Cupcakes cost \$3 each, and cookies cost \$2 each.

The basket costs \$ Write and solve a system of linear equations to find the number of cupcakes and cookies. Show you work/5.

## Systems of Linear Equations Translating a Word Problem into a System of Equations

Systems of Equations Word Problems Part 2 Date:_____ Subject: Pre-Algebra, Algebra I, or Algebra II • Write linear equations to model a real world situation. Stage 2 – Assessment Evidence example of a real life situation that would use systems of . WRITING Describe three ways to solve a system of linear equations.

In Exercises 4 – 6, (a) write a system of linear equations to represent the situation. Then, answer the question using (b) a table, (c) a graph, and (d) algebra. In order to find out if my students are ready, I give them a list of system of equations and ask them to identify, without solving, which method you would use to solve each problem.

I also ask for volunteers to create their own problem and come to the board and write down a system of equations. This is one of the most common types of system of equations problems. Remember that when you write a system of equations, you must have two different equations.

In this case, you have information about the number of questions AND the point value for each of the questions. MD Write and graph an equation for a line given the slope and the y‐intercept, the slope and a point on the line, or two points on the line, and translate between forms of linear equations.

ME Write and solve systems of two linear equations and inequalities in two variables.

Writing a System of Equations